Low defect density epitaxial wafer and a process for the preparation thereof

ABSTRACT

The present invention relates to single crystal silicon, in ingot or wafer form, which contains an axially symmetric region which is free of agglomerated intrinsic point defects, and a process for the preparation thereof. The process for growing the single crystal silicon ingot comprises controlling (i) a growth velocity, v, (ii) an average axial temperature gradient, G 0 , during the growth of a constant diameter portion of the crystal over a temperature range from solidification to a temperature of no less than about 1325° C., and (iii) a cooling rate of the crystal from a solidification temperature to about 1,050° C., in order to cause the formation of an axially symmetrical segment which is substantially free of agglomerated intrinsic point defects. This axially symmetric region extends inwardly from the circumferential edge of the ingot, has a width as measured from the circumferential edge radially toward the central axis of the ingot which is at least about three-tenths the length of the radius of the ingot, and has a length as measured along the central axis of at least about two-tenths the length of the constant diameter portion of the ingot.

REFERENCE TO RELATED APPLICATION

[0001] This application claims priority from U.S. provisionalapplication, U.S. Serial No. 60/041,845, filed on Apr. 9, 1997.

BACKGROUND OF THE INVENTION

[0002] The present invention generally relates to the preparation ofsemiconductor grade single crystal silicon which is used in themanufacture of electronic components. More particularly, the presentinvention relates to single crystal silicon ingots and wafers having anaxially symmetric region which is devoid of agglomerated intrinsic pointdefects, and a process for the preparation thereof.

[0003] Single crystal silicon, which is the starting material for mostprocesses for the fabrication of semiconductor electronic components, iscommonly prepared by the so-called Czochralski (“Cz”) method. In thismethod, polycrystalline silicon (“polysilicon”) is charged to a crucibleand melted, a seed crystal is brought into contact with the moltensilicon and a single crystal is grown by slow extraction. Afterformation of a neck is complete, the diameter of the crystal is enlargedby decreasing the pulling rate and/or the melt temperature until thedesired or target diameter is reached. The cylindrical main body of thecrystal which has an approximately constant diameter is then grown bycontrolling the pull rate and the melt temperature while compensatingfor the decreasing melt level. Near the end of the growth process butbefore the crucible is emptied of molten silicon, the crystal diametermust be reduced gradually to form an end-cone. Typically, the end-coneis formed by increasing the crystal pull rate and heat supplied to thecrucible. When the diameter becomes small enough, the crystal is thenseparated from the melt.

[0004] In recent years, it has been recognized that a number of defectsin single crystal silicon form in the crystal growth chamber as thecrystal cools after solidification. Such defects arise, in part, due tothe presence of an excess (i.e. a concentration above the solubilitylimit) of intrinsic point defects, which are known as vacancies andself-interstitials. Silicon crystals grown from a melt are typicallygrown with an excess of one or the other type of intrinsic point defect,either crystal lattice vacancies (“V”) or silicon self-interstitials(“I”). It has been suggested that the type and initial concentration ofthese point defects in the silicon are determined at the time ofsolidification and, if these concentrations reach a level of criticalsupersaturation in the system and the mobility of the point defects issufficiently high, a reaction, or an agglomeration events, will likelyoccur. Agglomerated intrinsic point defects in silicon can severelyimpact the yield potential of the material in the production of complexand highly integrated circuits.

[0005] Vacancy-type defects are recognized to be the origin of suchobservable crystal defects as D-defects, Flow Pattern Defects (FPDs),Gate Oxide Integrity (GOI) Defects, Crystal Originated Particle (COP)Defects, crystal originated Light Point Defects (LPDs), as well ascertain classes of bulk defects observed by infrared light scatteringtechniques such as Scanning Infrared Microscopy and Laser ScanningTomography. Also present in regions of excess vacancies are defectswhich act as the nuclei for ring oxidation induced stacking faults(OISF). It is speculated that this particular defect is a hightemperature nucleated oxygen agglomerate catalyzed by the presence ofexcess vacancies.

[0006] Defects relating to self-interstitials are less well studied.They are generally regarded as being low densities of interstitial-typedislocation loops or networks. Such defects are not responsible for gateoxide integrity failures, an important wafer performance criterion, butthey are widely recognized to be the cause of other types of devicefailures usually associated with current leakage problems.

[0007] The density of such vacancy and self-interstitial agglomerated deeffects in Czochralski silicon is conventionally within the range ofabout 1*10³/cm³ to about 1*10⁷/cm³. While these values are relativelylow, agglomerated intrinsic point defects are of rapidly increasingimportance to device manufacturers and, in fact, are now seen asyield-limiting factors in device fabrication processes.

[0008] To date, there generally exists three main approaches to dealingwith the problem of agglomerated intrinsic point defects. The firstapproach includes methods which focus on crystal pulling techniques inorder to reduce the number density of agglomerated intrinsic pointdefects in the ingot. This approach can be further subdivided into thosemethods having crystal pulling conditions which result in the formationof vacancy dominated material, and those methods having crystal pullingconditions which result in the formation of self-interstitial dominatedmaterial. For example, it has been suggested that the number density ofagglomerated defects can be reduced by (i) controlling v/G₀ to grow acrystal in which crystal lattice vacancies are the dominant intrinsicpoint defect, and (ii) influencing the nucleation rate of theagglomerated defects by altering (generally, by slowing down) thecooling rate of the silicon ingot from about 1100° C. to about 1050° C.during the crystal pulling process. While this approach reduces thenumber density of agglomerated defects, it does not prevent theirformation. As the requirements imposed by device manufacturers becomemore and more stringent, the presence of these defects will continue tobecome more of a problem.

[0009] Others have suggested reducing the pull rate, during the growthof the body of the crystal, to a value less than about 0.4 mm/minute.This suggestion, however, is also not satisfactory because such a slowpull rate leads to reduced throughput for each crystal puller. Moreimportantly, such pull rates lead to the formation of single crystalsilicon having a high concentration of self-interstitials. This highconcentration, in turn, leads to the formation of agglomeratedself-interstitial defects and all the resulting problems associated withsuch defects.

[0010] A second approach to dealing with the problem of agglomeratedintrinsic part defects includes methods which focus on the dissolutionor annihilation of agglomerated intrinsic point defects subsequent totheir formation. Generally, this is achieved by using high temperatureheat treatments of the silicon in wafer form. For example, Fusegawa etal. propose, in European Patent Application 503,815 A1, growing thesilicon ingot at a growth rate in excess of 0.8 mm/minute, and heattreating the wafers which are sliced from the ingot at a temperature inthe range of 1150° C. to 1280° C. to reduce the defect density in a thinregion near the wafer surface. The specific treatment needed will varydepending upon the concentration and location of agglomerated intrinsicpoint defects in the wafer. Different wafers cut from a crystal whichdoes not have a uniform axial concentration of such defects may requiredifferent post-growth processing conditions. Furthermore, such waferheat treatments are relatively costly, have the potential forintroducing metallic impurities into the silicon wafers, and are notuniversally effective for all types of crystal-related defects.

[0011] A third approach to dealing with the problem of agglomeratedintrinsic point defects is the epitaxial deposition of a thincrystalline layer of silicon on the surface of a single crystal siliconwafer. This process provides a single crystal silicon wafer having asurface which is substantially free of agglomerated intrinsic pointdefects. Epitaxial deposition, however, substantially increases the costof the wafer.

[0012] In view of these developments, a need continues to exist for amethod of single crystal silicon preparation which acts to prevent theformation of agglomerated intrinsic point defects by suppressing theagglomeration reactions which produce them. Rather than simply limitingthe rate at which such defects form, or attempting to annihilate some ofthe defects after they have formed, a method which acts to suppressagglomeration reactions would yield a silicon substrate that issubstantially free of agglomerated intrinsic point defects. Such amethod would also afford single crystal silicon wafers having epi-likeyield potential, in terms of the number of integrated circuits obtainedper wafer, without having the high costs associated with an epitaxialprocess.

SUMMARY OF THE INVENTION

[0013] Among the objects of the present invention, therefore, is theprovision of single crystal silicon in ingot or wafer form having anaxially symmetric region of substantial radial width which issubstantially free of defects resulting from an agglomeration of crystallattice vacancies or silicon self-interstitials; and the provision of aprocess for preparing a single crystal silicon ingot in which theconcentration of vacancies and self-interstitials is controlled in orderto prevent an agglomeration of intrinsic point defects in an axiallysymmetric segment of a constant diameter portion of the ingot, as theingot cools from the solidification temperature.

[0014] Briefly, therefore, the present invention is directed to aprocess for growing a single crystal silicon ingot in which the ingotcomprises a central axis, a seed-cone, an end-cone and a constantdiameter portion between the seed-cone and the end-cone having acircumferential edge and a radius extending from the central axis to thecircumferential edge. In the process, the ingot is grown from a siliconmelt and then cooled from the solidification temperature in accordancewith the Czochralski method. In particular, the process comprisescontrolling (i) a growth velocity, v, (ii) an average axial temperaturegradient, G₀, during the growth of the constant diameter portion of thecrystal over the temperature range from solidification to a temperatureof no less than about 1325° C., and (iii) the cooling rate of thecrystal from the solidification temperature to about 1,050° C. to causethe formation of an axially symmetrical segment which is substantiallyfree of agglomerated intrinsic point defects wherein the axiallysymmetric region extends inwardly from the circumferential edge of theingot, has a width as measured from the circumferential edge radiallytoward the central axis of the ingot which is at least aboutthree-tenths the length of the radius of ingot, and has a length asmeasured along the central axis of at least about two-tenths the lengthof the constant diameter portion of the ingot.

[0015] Other objects and features of this invention will be in partapparent and in part pointed out hereinafter.

BRIEF DESCRIPTION OF THE DRAWINGS

[0016]FIG. 1 is a graph which shows an example of how the initialconcentration of self-interstitials, [I], and vacancies, [V], changeswith an increase in the value of the ratio v/G₀, where v is the growthrate and G₀ is the average axial temperature gradient.

[0017]FIG. 2 is a graph which shows an example of how ΔG_(I), the changein free energy required for the formation of agglomerated interstitialdefects, increases as the temperature, T, decreases, for a given initialconcentration of self-interstitials, [I].

[0018]FIG. 3 is a graph which shows an example of how ΔG_(I), the changein free energy required for the formation of agglomerated interstitialdefects, decreases (as the temperature, T, decreases) as a result of thesuppression of the concentration of self-interstitials, [I], through themeans of radial diffusion. The solid line depicts the case for no radialdiffusion whereas the dotted line includes the effect of diffusion.

[0019]FIG. 4 is a graph which shows an example of how ΔG_(I), the changein free energy required for the formation of agglomerated interstitialdefects, is sufficiently decreased (as the temperature, T, decreases),as a result of the suppression of the concentration ofself-interstitials, [I], through the means of radial diffusion, suchthat an agglomeration reaction is prevented. The solid line depicts thecase for no radial diffusion whereas the dotted line includes the effectof diffusion.

[0020]FIG. 5 is a graph which shows an example of how the initialconcentration of self-interstitials, [I], and vacancies, [V], can changealong the radius of an ingot or wafer, as the valve of the ratio v/G₀decreases, due to an increase in the value of G₀. Note that at the V/Iboundary a transition occurs from vacancy dominated material toself-interstitial dominated material.

[0021]FIG. 6 is a top plan view of a single crystal silicon ingot orwater showing regions of vacancy, V, and self-interstitial, I, dominatedmaterials respectively, as well as the V/I boundary that exists betweenthem.

[0022]FIG. 7a is a graph which shows an example of how the initialconcentration of vacancies or self-interstitials changes as a functionof radial position due to radial diffusion of self-interstitials. Alsoshown is how such diffusion causes the location of the V/I boundary tomove closer to the center of the ingot (as a result of the recombinationof vacancies and self-interstitials), as well as the concentration ofself-interstitials, [I], to be suppressed.

[0023]FIG. 7b is a graph of ΔG_(I) as a function of radial positionwhich shows an example of how the suppression of self-interstitialconcentration, [I], (as depicted in FIG. 7a) is sufficient to maintainΔG_(I) everywhere to a value which is less than the critical value atwhich the silicon self-interstitial reaction occurs.

[0024]FIG. 7c is a graph which shows another example of how the initialconcentration of vacancies or self-interstitials changes as a functionof radial position due to radial diffusion of self-interstitials. Notethat, in comparison to FIG. 7a, such diffusion caused the location ofthe V/I boundary to be closer to the center of the ingot (as a result ofthe recombination of vacancies and self-interstitials), resulting in anincrease in the concentration of interstitials in the region outside ofthe V/I boundary.

[0025]FIG. 7d is a graph of ΔG_(I) as a function of radial positionwhich shows an example of how the suppression of self-interstitialconcentration, [I], (as depicted in FIG. 7c) is not sufficient tomaintain ΔG_(I) everywhere to a value which is less than the criticalvalue at which the silicon self-interstitial reaction occurs.

[0026]FIG. 7e is a graph which shows another example of how the initialconcentration of vacancies or self-interstitials chances as a functionof radial position due to radial diffusion of self-interstitials. Notethat, in comparison to FIG. 7a, increased diffusion resulted in greatersuppression the self-interstitial concentration.

[0027]FIG. 7f is a graph of ΔG_(I) as a function of radial positionwhich shows an example of how greater suppression of theself-interstitial concentration, [I], (as depicted in FIG. 7e) resultsin a greater degree of suppression in ΔG_(I), as compared to FIG. 7b.

[0028]FIG. 7g is a graph which shows another example of how the initialconcentration of vacancies or self-interstitials chances as a functionof radial position due to radial diffusion of self-interstitials. Notethat, in comparison to FIG. 7c, increased diffusion resulted in greatersuppression the self-interstitial concentration.

[0029]FIG. 7h is a graph of ΔG_(I) as a function of radial positionwhich shows an example of how greater suppression of theself-interstitial concentration, [I], (as depicted in FIG. 7g) resultsin a greater degree of suppression in ΔG_(I), as compared to FIG. 7d.

[0030]FIG. 7i is a graph which shows another example of how the initialconcentration of vacancies or self-interstitials changes as a functionof radial position due to radial diffusion of self-interstitials. Notethat in this example a sufficient quantity of self-interstitialsrecombine with vacancies, such that there is no longer avacancy-dominated region.

[0031]FIG. 7j is a graph of ΔG_(I) as a function of radial positionwhich shows an example of how radial diffusion of self-interstitials (asdepicted in FIG. 7i) is sufficient to maintain a suppression ofagglomerated interstitial defects everywhere along the crystal radius.

[0032]FIG. 8 is a longitudinal, cross-sectional view of a single crystalsilicon ingot showing, in detail, an axially symmetric region of aconstant diameter portion of the ingot.

[0033]FIG. 9 is a longitudinal, cross-sectional view of a segment of aconstant diameter portion of a single crystal silicon ingot, showing indetail axial variations in the width of an axially symmetric region.

[0034]FIG. 10 is a longitudinal, cross-sectional view of a segment of aconstant diameter portion of a single crystal silicon ingot havingaxially symmetric region of a width which is less than the radius of theingot, showing in detail that this region further contains a generallycylindrical region of vacancy dominated material.

[0035]FIG. 11 is a latitudinal, cross-sectional view of the axiallysymmetric region depicted in FIG. 10.

[0036]FIG. 12 is a longitudinal, cross-sectional view of a segment of aconstant diameter portion of a single crystal silicon ingot having anaxially symmetric region of a width which is equal to the radius of theingot, showing in detail that this region is a generally cylindricalregion of self-interstitial dominated material which is substantiallyfree of agglomerated intrinsic point defects.

[0037]FIG. 13 is an image produced by a scan of the minority carrierlifetime of an axial cut of the ingot following a series of oxygenprecipitation heat treatments, showing in detail a generally cylindricalregion of vacancy dominated material, a generally annular shaped axiallysymmetric region of self-interstitial dominated material, the V/Iboundary present between them, and a region of agglomerated interstitialdefects.

[0038]FIG. 14 is a graph of pull rate (i.e. seed lift) as is a functionof crystal length, showing how the pull rate is decreased linearly overa portion of the length of the crystal.

[0039]FIG. 15 is an image produced by a scan of the minority carrierlifetime of an axial cut of the ingot following a series of oxygenprecipitation heat treatments, as described in Example 1.

[0040]FIG. 16 is a graph of pull rate as a function of crystal lengthfor each of four single crystal silicon ingots, labeled 1-4respectively, which are used to yield a curve, labeled v*(Z), asdescribed in Example 1.

[0041]FIG. 17 is a graph of the average axial temperature gradient atthe melt/solid interface, G₀, as a function of radial position, for twodifferent cases as described in Example 2.

[0042]FIG. 18 is a graph of the initial concentration of vacancies, [V],or self-interstitials, [I], as a function of radial position, for twodifferent cases as described Example 2.

[0043]FIG. 19 is a graph of temperature as a function of axial position,showing the axial temperature profile in ingots for two different casesas described in Example 3.

[0044]FIG. 20 is a graph of the self-interstitial concentrationsresulting from the two cooling conditions illustrated in FIG. 19 and asmore fully described in Example 3.

[0045]FIG. 21 is an image produced by a scan of the minority carrierlifetime of an axial cut of an entire ingot following a series of oxygenprecipitation heat treatments, as described in Example 4.

[0046]FIG. 22 is a graph illustrating the position of the V/I boundaryas a fun on of the length of the single crystal silicon ingot, asdescribed in Example 5.

[0047]FIG. 23a is an image produced by a scan of the minority carrierlifetime of an axial cut of a segment of an ingot, ranging from about100 mm to about 250 mm from the shoulder of the ingot, following aseries of oxygen precipitation heat treatments, as described in Example6.

[0048]FIG. 23b is an image produced by a scan of the minority carrierlifetime of an axial cut of a segment of an ingot, ranging from about250 mm to about 400 mm from the shoulder of the ingot, following aseries of oxygen precipitation heat treatments, as described in Example6.

[0049]FIG. 24 is a graph illustrating the axial temperature profile foran ingot in four different hot zone configurations.

[0050]FIG. 25 is a graph of the axial temperature gradient, G₀, atvarious axial positions for an ingot, as described in Example 7.

[0051]FIG. 26 is a graph of the radial variations in the average axialtemperature gradient, G₀, at various for an ingot, as described inexample 7.

[0052]FIG. 27 is a graph illustrating the relationship between the widthof the axially symmetric region and the cooling rate, as described inExample 7.

[0053]FIG. 28 is a photograph of an axial cut of a segment of an ingot,ranging from about 235 mm to about 350 mm from the shoulder of theingot, following copper decoration and a defect-delineating etch,described in Example 7.

[0054]FIG. 29 is a photograph of an axial cut of a segment of an ingot,ranging from about 305 mm to about 460 mm from the shoulder of theingot, following copper decoration and a defect-delineating etch,described in Example 7.

[0055]FIG. 30 is a photograph of an axial cut of a segment of an ingot,ranging from about 140 mm to about 275 mm from the shoulder of theingot, following copper decoration and a defect-delineating etch,described in Example 7.

[0056]FIG. 31 is a photograph of an axial cut of a segment of an ingot,ranging from about 600 mm to about 730 mm from the shoulder of theingot, following copper decoration and a defect-delineating etch,described in Example 7.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0057] Based upon experimental evidence to date, it appears that thetype and initial concentration of intrinsic point defects is initiallydetermined as the ingot cools from the temperature of solidification(i.e., about 1410° C.) to a temperature greater than 1300° C. (i.e., atleast about 1325° C., at least about 1350° C. or even at least about1375° C.). That is, the type and initial concentration of these defectsare controlled by the ratio v/G₀, where v is the growth velocity and G₀is the average axial temperature gradient over this temperature range.

[0058] Referring to FIG. 1, for increasing values of v/G₀, a transitionfrom decreasingly self-interstitial dominated growth to increasinglyvacancy dominated growth occurs near a critical value of v/G₀ which,based upon currently available information, appears to be about 2.1×10⁻⁵cm²/sK, where G₀ is determined under conditions in which the axialtemperature gradient is constant within the temperature range definedabove. At this critical value, the concentrations of these intrinsicpoint defects are at equilibrium.

[0059] As the value of v/G₀ exceeds the critical value, theconcentration of vacancies increases. Likewise, as the value of v/G₀falls below the critical value, the concentration of self-interstitialsincreases. If these concentrations reach a level of criticalsupersaturation in the system, and if the mobility of the point defectsis sufficiently high, a reaction, or an agglomeration event, will likelyoccur. Agglomerated intrinsic point defects in silicon can severelyimpact the yield potential of the material in the production of complexand highly integrated circuits.

[0060] In accordance with the present invention, it has been discoveredthat the reaction in which silicon self-interstitial atoms react toproduce agglomerated interstitial defects can be suppressed. Withoutbeing bound to any particular theory, it is believed that theconcentration of self-interstitials is controlled during the growth andcooling of the crystal ingot in the process of the present invention,such that the change in free energy of the system never exceeds acritical value at which the agglomeration reaction spontaneously occursto produce agglomerated interstitial defects.

[0061] In general, the change in system free energy available to drivethe reaction in which agglomerated interstitial defects are formed fromsilicon self-interstitials in single crystal silicon is governed byEquation (I): $\begin{matrix}{{\Delta \quad G_{I}} = {{kT}\quad {\ln \left( \frac{\lbrack I\rbrack}{\lbrack I\rbrack^{eq}} \right)}}} & (I)\end{matrix}$

[0062] wherein

[0063] ΔG_(I) is the change in free energy,

[0064] k is the Boltzmann constant,

[0065] T is the temperature in K,

[0066] [I] is the concentration of self-interstitials at a point inspace and time in the single crystal silicon, and

[0067] [I]^(eq) is the equilibrium concentration of self-interstitialsat the same point in space and time at which [I] occurs and at thetemperature, T.

[0068] According to this equation, for a given concentration ofself-interstitials, [I], a decrease in the temperature, T, generallyresults in an increase in ΔG_(I) due to a sharp decrease in [I]^(eq)with temperature.

[0069]FIG. 2 schematically illustrates the change in ΔG_(I) and theconcentration of silicon self-interstitials for an ingot which is cooledfrom the temperature of solidification without simultaneously employingsome means for suppression of the concentration of siliconself-interstitials. As the ingot cools, ΔG_(I) increases according toEquation (I), due to the increasing supersaturation of [I], and theenergy barrier for the formation of agglomerated interstitial defects isapproached. As cooling continues, this energy barrier is eventuallyexceeded, at which point a reaction occurs. This reaction results in theformation of agglomerated interstitial defects and the concomitantdecrease in ΔG_(I) as the supersaturated system is relaxed, i.e., as theconcentration of [I] decreases.

[0070] The agglomeration of self-interstitials can be avoided as theingot cools from the temperature of solidification by maintaining thefree energy of the silicon self-interstitial system at a value which isless than that at which an agglomeration reaction will occur. In otherwords, the system can be controlled so as to never become criticallysupersaturated. This can be achieved by establishing an initialconcentration of self-interstitials (controlled by v/G₀(r) ashereinafter defined) which is sufficiently low such that criticalsupersaturation is never achieved. However, in practice suchconcentrations are difficult to achieve across an entire crystal radiusand, in general, therefore, critical supersaturation may be avoided bysuppressing the initial silicon self-interstitial concentrationsubsequent to crystal solidification, i.e., subsequent to establishingthe initial concentration determined by v/G₀(r).

[0071]FIGS. 3 and 4 schematically illustrate two possible effects ofsuppressing [I] upon the increase in ΔG_(I) as the ingot of FIG. 2 iscooled from the temperature of solidification. In FIG. 3, thesuppression of [I] results in a decrease in the rate of increase ofΔG_(I) but, in this case, the suppression is insufficient to maintainΔG_(I) everywhere at a value which is less than the critical value atwhich the reaction occurs; as a result, the suppression merely serves toreduce the temperature at which the reaction occurs. In FIG. 4, anincreased suppression of [I] is sufficient to maintain ΔG_(I) everywhereto a value which is less than the critical value at which the reactionoccurs; the suppression, therefore, inhibits the formation of defects.

[0072] Surprisingly, it has been found that due to the relatively largemobility of self-interstitials, which is generally about 10⁻⁴cm²/second, it is possible to effect the suppression over relativelylarge distances, i.e. distances of about 5 cm to about 10 cm or more, bythe radial diffusion of self-interstitials to sinks located at thecrystal surface or to vacancy dominated regions located within thecrystal. Radial diffusion can be effectively used to suppress theconcentration of self-interstitials, provided sufficient time is allowedfor the radial diffusion of the initial concentration of intrinsic pointdefects. In general, the diffusion time will depend upon the radialvariation in the initial concentration of self-interstitials, withlesser radial variations requiring shorter diffusion times.

[0073] Typically, the average axial temperature gradient, G₀, increasesas a function of increasing radius for single crystal silicon, which isgrown according to the Czochralski method. This means that the value ofv/G₀ is typically not singular across the radius of an ingot. As aresult of this variation, the type and initial concentration ofintrinsic point defects is not constant. If the critical value of v/G₀,denoted in FIGS. 5 and 6 as the V/I boundary 2, is reached at some pointalong the radius 4 of the ingot, the material will switch from beingvacancy dominated to self-interstitial dominated. In addition, the ingotwill contain an axially symmetric region of self-interstitial dominatedmaterial 6 (in which the initial concentration of siliconself-interstitial atoms increases as a function of increasing radius),surrounding a generally cylindrical region of vacancy dominated material8 (in which the initial concentration of vacancies decreases as afunction of increasing radius).

[0074]FIGS. 7a and 7 b schematically illustrate the effect ofsuppressing [I] upon the increase in ΔG_(I) as an ingot is cooled fromthe temperature of solidification in accordance with one embodiment ofthe present invention. When the ingot is pulled in accordance with theCzochralski method, the ingot contains an axially symmetric region ofinterstitial dominated material extending from the edge of the ingot tothe position along the radius at which the V/I boundary occurs and agenerally cylindrical region of vacancy dominated material extendingfrom the center of the ingot to the position along the radius at whichthe V/I boundary occurs. As the ingot is cooled from the temperature ofsolidification, radial diffusion of interstitial atoms causes a radiallyinward shift in the V/I boundary due to a recombination ofself-interstitials with vacancies and a significant suppression of theself-interstitial concentration outside the V/I boundary. In addition,radial diffusion of self-interstitials to the surface of the crystalwill occur as the crystal cools. The surface of the crystal is capableof maintaining near equilibrium point defect concentrations as thecrystal cools. As a result, the suppression of [I] is sufficient tomaintain ΔG_(I) everywhere to a value which is less than the criticalvalue at which the silicon self-interstitial reaction occurs.

[0075] Referring now to FIGS. 8 and 9, in the process of the presentinvention a single crystal silicon ingot 10 is grown in accordance withthe Czochralski method. The silicon ingot comprises a central axis 12, aseed-cone 14, an end-cone 16 and a constant diameter portion 18 betweenthe seed-cone and the end-cone. The constant diameter portion has acircumferential edge 20 and a radius 4 extending from the central axisto the circumferential edge. The process comprises controlling thegrowth conditions, including growth velocity, v, the average axialtemperature gradient, G₀, and the cooling rate, to cause the formationof an axially symmetric region 6 which, upon cooling of the ingot fromthe solidification temperature, is substantially free of agglomeratedintrinsic point defects.

[0076] In one embodiment, the growth conditions are controlled tomaintain the V/I boundary 2 at a position which maximizes the volume ofthe axially symmetric region 6 relative to the volume of the constantdiameter portion 18 of the ingot 10. In general, therefore, in thisembodiment it is preferred that the axially symmetric region have awidth 22 (as measured from the circumferential edge radially toward thecentral axis of the ingot) and a length 24 (as measured along thecentral axis of the ingot) which equals the radius 4 and length 26,respectively, of the constant diameter portion of the ingot. As apractical matter, however, operating conditions and crystal pullerhardware constraints may dictate that the axially symmetric regionoccupy a lesser proportion of the constant diameter portion of theingot. In general, therefore, the axially symmetric region in thisembodiment preferably has a width of at least about 30%, more preferablyat least about 40%, still more preferably at least about 60%, and mostpreferably at least about 80% of the radius of the constant diameterportion of the ingot. In addition, the axially symmetric region extendsover a length of at least about 20%, preferably at least about 40%, morepreferably at least about 60%, and still more preferably at least about80% of the length of the constant diameter portion of the ingot.

[0077] Referring to FIG. 9, the width 22 of the axially symmetric region6 may have some variation along the length of the central axis 12. Foran axially symmetric region of a given length, therefore, the width isdetermined by measuring the distance from the circumferential edge 20 ofthe ingot 10 radially toward a point which is farthest from the centralaxis. In other words, the width 22 is measured such that the minimumdistance within the given length 24 of the axially symmetric region 6 isdetermined.

[0078] Referring now to FIGS. 10 and 11, when the axially symmetricregion 6 of the constant diameter portion 18 of the ingot 10 has a width22 which is less than the radius 4 of the constant diameter portion, theregion is generally annular in shape. A generally cylindrical region ofvacancy dominated material 8, which is centered about the central axis12, is located radially inward of the generally annular shaped segment.Referring to FIG. 12, it is to be understood that when the width 22 ofthe axially symmetric region 6 is equal to the radius 4 of the constantdiameter portion 18, the region does not contain this vacancy dominatedregion; rather, the axially symmetric region itself is generallycylindrical and contains self-interstitial dominated material which issubstantially free of agglomerated intrinsic point defects.

[0079] While it is generally preferred that the crystal growthconditions be controlled to maximize the width of the interstitialdominated region, there may be limits for a given crystal puller hotzone design. As the V/I boundary is moved closer to the central crystalaxis, provided the cooling conditions and G₀(r) do not change, whereG₀(r) is the radial variation of G₀, the minimum amount of radialdiffusion required increases. In these circumstances, there may be aminimum radius of the vacancy dominated region which is required tosuppress the formation of agglomerated interstitial defects by radialdiffusion.

[0080]FIGS. 7c and 7 d schematically illustrate an example in which theminimum radius of the vacancy dominated region is exceeded. In thisexample, the cooling conditions and G₀(r) are the same as those employedfor the crystal of FIGS. 7a and 7 b in which there was sufficientoutdiffusion to avoid agglomerated interstitial defects or the positionof the V/I boundary illustrated. In FIGS. 7c and 7 d, the position ofthe V/I boundary is moved closer to the central axis (relative to FIGS.7a and 7 b) resulting in an increase in the concentration ofinterstitials in the region outside of the V/I boundary. As a result,more radial diffusion is required to sufficiently suppress theinterstitial concentration. If sufficient outdiffusion is not achieved,the system ΔG_(I) will increase beyond the critical value and thereaction which produces agglomerated interstitial defects will occur,producing a region of these defects in an annular region between the V/Iboundary and the edge of the crystal. The radius of the V/I boundary atwhich this occurs is the minimum radius for the given hot zone. Thisminimum radius is decreased if more radial diffusion of interstitials isallowed.

[0081]FIGS. 7e, 7 f, 7 g and 7 h illustrate the effect of an increasedradial outdiffusion on interstitial concentration profiles and the riseof system ΔG_(I) for a crystal grown with the same initial vacancy andinterstitial concentration profiles as the crystal exemplified in FIGS.7a, 7 b, 7 c and 7 d. Increased radial diffusion of interstitialsresults in a greater suppression of interstitial concentration, thussuppressing the rise in the system ΔG_(I) to a greater degree than inFIGS. 7a, 7 b, 7 c and 7 d. In this case the system ΔG_(I) is notexceeded for the smaller radius of the V/I boundary.

[0082]FIGS. 7i and 7 j illustrate an example in which sufficient radialdiffusion is allowed such that the minimum radius is reduced to zero byinsuring sufficient radial diffusion to achieve a suppression ofagglomerated interstitial defects everywhere along the crystal radius.

[0083] In one embodiment of the process of the present invention, theinitial concentration of silicon self-interstitial atoms is controlledin the axially symmetric, self-interstitial dominated region of theingot. Referring again to FIG. 1, in general, the initial concentrationof silicon self-interstitial atoms is controlled by controlling thecrystal growth velocity, v, and the average axial temperature gradient,G₀, such that the value of the ratio v/G₀ is relatively near thecritical value of this ratio, at which the V/I boundary occurs. Inaddition, the average axial temperature gradient, G₀, can be establishedsuch that the variation of G₀, i.e. G₀(r), (and thus, v/G₀(r)) as afunction of the ingot radius is also controlled.

[0084] The growth velocity, v, and the average axial temperaturegradient, G₀, (as previously defined) are typically controlled such thatthe ratio v/G₀ ranges in value from about 0.5 to about 2.5 times thecritical value of v/G₀ (i.e., about 1×10⁻⁵ cm²/sK to about 5×10⁻⁵ cm²/sKbased upon currently available information for the critical value ofv/G₀). Preferably, the ratio v/G₀ will range in value from about 0.6 toabout 1.5 times the critical value of v/G₀ (i.e., about 1.3×10⁻⁵ cm²/sKto about 3×10⁻⁵ cm²/sK based upon currently available information forthe critical value of v/G₀). Most preferably, the ratio v/G₀ will rangein value from about 0.75 to about 1 times the critical value of v/G₀(i.e., about 1.6×10⁻⁵ cm²/sK to about 2.1×10⁻⁵ cm²/sK based uponcurrently available information for the critical value of v/G₀). Theseratios are achieved by independent control of the growth velocity, v,and the average axial temperature gradient, G₀.

[0085] In general, control of the average axial temperature gradient,G₀, may be achieved primarily through the design of the “hot zone” ofthe crystal puller, i.e. the graphite (or other materials) that makes upthe heater, insulation, heat and radiation shields, among other things.Although the design particulars may vary depending upon the make andmodel of the crystal puller, in general, G₀ may be controlled using anyof the means currently known in the art for controlling heat transfer atthe melt/solid interface, including reflectors, radiation shields, purgetubes, light pipes, and heaters. In general, radial variations in G₀ areminimized by positioning such an apparatus within about one crystaldiameter above the melt/solid interface. G₀ can be controlled further byadjusting the position of the apparatus relative to the melt andcrystal. This is accomplished either by adjusting the position of theapparatus in the hot zone, or by adjusting the position of the meltsurface in the hot zone. In addition, when a heater is employed, G₀ maybe further controlled by adjusting the power supplied to the heater.Any, or all, of these methods can he used during a batch Czochralskiprocess in which melt volume is depleted during the process.

[0086] It is generally preferred for some embodiments of the presentinvention that the average axial temperature gradient, G₀, be relativelyconstant as a function of diameter of the ingot. However, it should benoted that as improvements in hot zone design allow for variations in G₀to be minimized, mechanical issues associated with maintaining aconstant growth rate become an increasingly important factor. This isbecause the growth process becomes much more sensitive to any variationin the pull rate, which in turn directly effects the growth rate, v. Interms of process control, this means that it is favorable to have valuesfor G₀ which differ over the radius of the ingot. Significantdifferences in the value of G₀, however, can result in a largeconcentration of self-interstitials generally increasing toward thewafer edge and, thereby, increase the difficultly in avoiding theformation of agglomerated intrinsic point defects.

[0087] In view of the foregoing, the control of G₀ involves a balancebetween, minimizing radial variations in G₀ and maintaining favorableprocess control conditions. Typically, t the pull rate after about onediameter of the crystal length will range from about 0.2 mm/minute toabout 0.8 mm/minute. Preferably, the pull rate will range from about0.25 mm/minute to about 0.6 mm/minute and, more preferably, from about0.3 mm/minute to about 0.5 mm/minute. It is to be noted that the pullrate is dependent upon both the crystal diameter and crystal pullerdesign. The stated ranges are typical for 200 mm diameter crystals. Ingeneral, the pull rate will decrease as the crystal diameter increases.However, the crystal puller may be designed to allow pull rates inexcess of those stated here. As a result, most preferably the crystalpuller will be designed to enable the pull rate to be as fast aspossible while still allowing for the formation of an axially symmetricregion in accordance with the present invention.

[0088] In a second and preferred embodiment, the amount ofself-interstitial diffusion is controlled by controlling the coolingrate as the ingot is cooled from the solidification temperature (about1410° C.) to the temperature at which silicon self-interstitials becomeimmobile, for commercially practical purposes. Siliconself-interstitials appear to be extremely mobile at temperatures nearthe solidification temperature of silicon, i.e. about 1410° C. Thismobility, however, decreases as the temperature of the single crystalsilicon ingot decreases. Generally, the diffusion rate ofself-interstitials slows such a considerable degree that they areessentially immobile for commercially practical time periods attemperatures less than about 700° C., and perhaps temperatures as greatas 800° C., 900° C., 1000° C., or even 1050° C.

[0089] It is to be noted in this regard that, although the temperatureat which a self-interstitial agglomeration reaction occurs may in theoryvary over a wide range of temperatures, as a practical matter this rangeappears to be relatively narrow for conventional, Czochralski grownsilicon. This is a consequence of the relatively narrow range of initialself-interstitial concentrations which are typically obtained in silicongrown according to the Czochralski method. In general, therefore, aself-interstitial agglomeration reaction may occur, if at all, attemperatures within the range of about 1100° C. to about 800° C., andtypically at a temperature of about 1050° C.

[0090] Within the range of temperatures at which self-interstitialsappear to be mobile, and depending upon the temperature in the hot zone,the cooling rate will typically range from about 0.1° C./minute to about3° C./minute. Preferably, the cooling rate will range from about 0.1°C./minute to about 1.5° C./minute, more preferably from about 0.1°C./minute to about 1° C./minute, and still more preferably from about0.1° C./minute to about 0.5° C./minute. Stated another way, to maximizethe width of the axially symmetric region it is generally preferred thatthe silicon reside at a temperature in excess of about 1050° C. for aperiod of (i) at least about 5 hours, preferably at least about 10hours, and more preferably at least about 15 hours for 150 mm nominaldiameter silicon crystals, (ii) at least about 5 hours, preferably atleast about 10 hours, more preferably at least about 20 hours, stillmore preferably at least about 25 hours, and most preferably at leastabout 30 hours for 200 mm nominal diameter silicon crystals, and (iii)at least about 20 hours, preferably at least about 40 hours, morepreferably at least about 60 hours, and most preferably at least about75 hours for silicon crystals having a nominal diameter greater than 200mm. Referring to FIG. 24, as can be seen from these axial temperatureprofiles for different hot zone configurations, control of the coolingrate can be achieved by using any means currently known in the art forminimizing heat transfer in the hot zone, including the use ofinsulators, heaters, radiation shields, and magnetic fields.

[0091] By controlling the cooling rate of the ingot within a range oftemperatures in which self-interstitials appear to be mobile, theself-interstitials may be given more time to diffuse to sinks located atthe crystal surface, or to vacancy dominated regions, where they may beannihilated. The concentration of such interstitials may therefore besuppressed, which act to prevent an agglomeration event from occurring.Utilizing the diffusivity of interstitials by controlling the coolingrate acts to relax the otherwise stringent v/G₀ requirements that may berequired in order to obtain an axially symmetric region free ofagglomerated defects. Stated another way, as a result of the fact thatthe cooling rate may be controlled in order to allow interstitials moretime to diffuse, a large range of v/G₀ values, relative to the criticalvalue, are acceptable for purposes of obtaining an axially symmetricregion free of agglomerated defects.

[0092] To achieve such cooling rates over appreciable lengths of theconstant diameter portion of the crystal, consideration must also begiven to the growth process of the end-cone of the ingot, as well as thetreatment of the ingot once end-cone growth is complete. Typically, uponcompletion of the growth of the constant diameter portion of the ingot,the pull rate will be increased in order to begin the tapering necessaryto form the end-cone. However, such an increase in pull rate will resultin the lower segment of the constant diameter portion cooling morequickly within the temperature range in which interstitials aresufficiently mobile, as discussed above. As a result, these interstitials may not have sufficient time to diffuse to sinks to be annihilated;that is, the concentration in this lower segment may not be suppressedto a sufficient degree and agglomeration of interstitial defects mayresult.

[0093] In order to prevent the formation of such defects from occurringin this lower segment of the ingot, it is therefore preferred thatconstant diameter portion of the ingot have a uniform thermal history inaccordance with the Czochralski method. A uniform thermal history may beachieved by pulling the ingot from the silicon melt at a relativelyconstant rate during the growth of not only the constant diameterportion, but also during the growth of the end-cone of the crystal andpossibly subsequent to growth of the end-cone. The relatively constantrate may be achieved, for example, by (i) reducing the rates of rotationof the crucible and crystal during the growth of the end-cone relativeto the crucible and crystal rotation rates during the growth of theconstant diameter portion of the crystal, and/or (ii) increasing thepower supplied to the heater used to heat the silicon melt during thegrowth of the end-cone relative to the power conventionally suppliedduring end-cone growth. These additional adjustments of the processvariables may occur either individually or in combination.

[0094] When the growth of the end-cone is initiated, a pull rate for theend-cone is established such that, any segment of the constant diameterportion of the ingot which remains at a temperature in excess of about1050° C. experiences the same thermal history as other segment(s) of theconstant diameter portion of the ingot which contain an axiallysymmetric region free of agglomerated intrinsic point defects which havealready cooled to a temperature of less than about 1050° C.

[0095] As previously noted, a minimum radius of the vacancy dominatedregion exists for which the suppression of agglomerated interstitialdefects may be achieved. The value of the minimum radius depends onv/G₀(r) and the cooling rate. As crystal puller and hot zone designswill vary, the ranges presented above for v/G₀(r), pull rate, andcooling rate will also vary. Likewise these conditions may vary alongthe length of a growing crystal. Also as noted above, the width of theinterstitial dominated region free of agglomerated interstitial defectsis preferably maximized. Thus, it is desirable to maintain the width ofthis region to a value which is as close as possible to, withoutexceeding, the difference between the crystal radius and the minimumradius of the vacancy dominated region along the length of the growingcrystal in a given crystal puller.

[0096] The optimum width of the axially symmetric region and therequired optimal crystal pulling rate profile for a given crystal pullerhot zone design may be determined empirically. Generally speaking, thisempirical approach involves first obtaining readily available data onthe axial temperature profile for an ingot grown in a particular crystalpuller, as well as the radial variations in the average axialtemperature gradient for an ingot grown in the same puller.Collectively, this data is used to pull one or more single crystalsilicon ingots, which are then analyzed for the presence of agglomeratedinterstitial defects. In this way, an optimum pull rate profile can bedetermined.

[0097]FIG. 13 is an image produced by a scan of the minority carrierlifetime of an axial cut of a section of a 200 mm diameter sot followinga series of oxygen precipitation heat-treatments which reveal defectdistribution patterns. It depicts an example in which a near-optimumpull rate profile is employed for a given crystal puller hot zonedesign. In this example, a transition occurs from a v/G₀(r) at which themaximum width of the interstitial dominated region is exceeded(resulting in the generation of regions of agglomerated interstitialdefects 28) to an optimum v/G₀(r) at which the axially symmetric regionhas the maximum width.

[0098] In addition to the radial variations in v/G₀ resulting from anincrease in G₀ over the radius of the ingot, v/G₀ may also vary axiallyas a result of a change in v, or as a result of natural variations in G₀due to the Czochralski process. For a standard Czochralski process, v isaltered as the pull rate is adjusted throughout the growth cycle, inorder to maintain the ingot at a constant diameter. These adjustments,or changes, in the pull rate in turn cause v/G₀ to vary over the lengthof the constant diameter portion of the ingot. In accordance with theprocess of the present invention, the pull rate is therefore controlledin order to maximize the width of the axially symmetric region of theingot. As a result, however, variations in the radius co the ingot mayoccur. In order to ensure that the resulting ingot has a constantdiameter, the ingot is therefore preferably grown to a diameter largerthan that which is desired. The ingot is then subjected to processesstandard in the art to remove excess material from the surface, thusensuring that an ingot having a constant diameter portion is obtained.

[0099] For an ingot prepared in accordance with the process of thepresent invention and having a V/I boundary, i.e. an ingot containingmaterial which is vacancy dominated, experience has shown that lowoxygen content material, i.e., less than about 13 PMMA (parts permillion atomic, ASTM standard F-121-83), is preferred. More preferably,the single crystal silicon contains less than about 12 PPMA oxygen,still more preferably less than about 11 PPMA oxygen, and mostpreferably less than about 10 PPMA oxygen. This is because, in medium tohigh oxygen contents wafers, i.e., 14 PPMA to 18 PPMA, the formation ofoxygen-induced stacking faults and bands of enhanced oxygen clusteringjust inside the V/I boundary becomes more pronounced. Each of these area potential source for problems in a given integrated circuitfabrication process. However, it is to be noted that, when the axiallysymmetric region has a width about equal to the radius of the ingot, theoxygen content restriction is removed; this is because, given that novacancy type material is present, the formation of such faults andclusters will not to occur.

[0100] The effects of enhanced oxygen clustering may be further reducedby a number of methods, used singularly or in combination. For example,oxygen precipitate nucleation centers typically form in silicon which isannealed at a temperature in the range of about 350° C. to about 750° C.For some applications, therefore, it may be preferred that the crystalbe a “short” crystal, that is, a crystal which has been grown in aCzochralski process until the seed end has cooled from the melting pointof silicon (about 1410° C.) to about 750° C. after which the ingot israpidly cooled. In this way, the time spent in the temperature rangecritical for nucleation center formation is kept to a minimum and theoxygen precipitate nucleation centers nave inadequate time to form inthe crystal puller.

[0101] Preferably, however, oxygen precipitate nucleation centers formedduring the growth of the single crystal are dissolved by annealing thesingle crystal silicon. Provided they have not been subjected to astabilizing heat-treatment, oxygen precipitate nucleation centers can beannealed out of silicon by rapidly heating the silicon to a temperatureof at least about 875° C., and preferably continuing to increase thetemperature to at least 1000° C., at least 1100° C., or more. By thetime the silicon reaches 1000° C., substantially all (e.g., >99%) ofsuch defects have annealed out. It is important that the wafers berapidly heated to these temperatures, i.e., that the rate of temperatureincrease be at least about 10° C. per minute and more preferably atleast about 50° C. per minute. Otherwise, some or all of the oxygenprecipitate nucleation centers may be stabilized by the heat-treatment.Equilibrium appears to be reached in relatively short periods of time,i.e., on the order of about 60 seconds or less. Accordingly, oxygenprecipitate nucleation centers in the single crystal silicon may bedissolved by annealing it at a temperature of at least about 875° C.,preferably at least about 950° C., and more preferably at least about1100° C., for a period of at least about 5 seconds, and preferably atleast about 10 minutes.

[0102] The dissolution may be carried out in a conventional furnace orin a rapid thermal annealing (RTA) system. The rapid thermal anneal ofsilicon may be carried out in any of a number of commercially availablerapid thermal annealing (“RTA”) furnaces in which wafers areindividually heated by banks of high power lamps. RTA furnaces arecapable of rapidly heating a silicon wafer, e.g., they are capable ofheating a wafer from room temperature to 1200° C. in a few seconds. Onesuch commercially available RTA furnace is the model 610 furnaceavailable from AG Associates (Mountain View, Calif.). In addition, thedissolution may be carried out on silicon ingots or on silicon wafers,preferably wafers.

[0103] It is to be noted that wafers prepared in accordance with thepresent invention are suitable for use as substrates upon which anepitaxial layer may be deposited. Epitaxial deposition may be performedby means common in the art.

[0104] Furthermore, it is also to be noted that wafers prepared inaccordance with the present invention are suitable for use incombination with hydrogen or argon annealing treatments, such as thetreatments described in European Patent Application No. 503,816 A1.

[0105] Detection of Agglomerated Defects

[0106] Agglomerated defects may be detected by a number of differenttechniques. For example, flow pattern defects, or D-defects, aretypically detected by preferentially etching the single crystal siliconsample in a Secco etch solution for about 30 minutes, and thensubjecting the sample to microscopic inspection. (see, e.g., H.Yamagishi et al., Semicond. Sci. Technol. 7, A135 (1992)). Althoughstandard for the detection of agglomerated vacancy defects, this processmay also be used to detect agglomerated interstitial defects. When thistechnique is used, such defects appear as large pits on the surface ofthe sample when present.

[0107] Agglomerated defects may also be detected using laser scatteringtechniques, such as laser scattering tomography, which typically have alower defect density detection limit that other etching techniques.

[0108] Additionally, agglomerated intrinsic point defects may bevisually detect by decorating these defects with a metal capable ofdiffusing into the single crystal silicon matrix upon the application ofheat. Specifically, single crystal silicon samples, such as wafers,slugs or slabs, may be visually inspected for the presence or suchdefects by first coating a surface of the sample with a compositioncontaining a metal capable of decorating these defects, such as aconcentrated solution of copper nitrate. The coated sample is thenheated to a temperature between about 900° C. and about 1000° C. forabout 5 minutes to about 15 minutes in order to diffuse the metal intothe sample. The heat treated sample is then cooled to room temperature,thus causing the metal to become critically supersaturated andprecipitate at sites within the sample matrix at which defects arepresent.

[0109] After cooling, the sample is first subjected to a non-defectdelineating etch, in order to remove surface residue and precipitants,by treating the sample with a bright etch solution for about 8 to about12 minutes. A typical bright etch solution comprises about 55 percentnitric acid (70% solution by weight), about 20 percent hydrofluoric acid(49% solution by weight), and about 25 percent hydrochloric acid(concentrated solution).

[0110] The sample is then rinsed with deionized water and subjected to asecond etching step by immersing the sample in, or treating it with, aSecco or Wright etch solution for about 35 to about 55 minutes.Typically, the sample will be etched using a Secco etch solutioncomprising about a 1:2 ratio of 0.15 M potassium dichromate andhydrofluoric acid (49% solution by weight). This etching step acts toreveal, or delineate, agglomerated defects which may be present.

[0111] Definitions

[0112] As used herein, the following phrases or terms shall have thegiven meanings: “agglomerated intrinsic point defects” mean defectscaused (i) by the reaction in which vacancies agglomerate to produceD-defects, flow pattern defects, gate oxide integrity defects, crystaloriginated particle defects, crystal originated light point defects, andother such vacancy related defects, or (ii) by the reaction in whichself-interstitials agglomerate to produce dislocation loops andnetworks, and other such self-interstitial related defects;“agglomerated interstitial defects” shall mean agglomerated intrinsicpoint defects caused by the reaction in which silicon self-interstitialatoms agglomerate; “agglomerated vacancy defects” shall meanagglomerated vacancy point defects caused by the reaction in whichcrystal lattice vacancies agglomerate; “radius” means the distancemeasured from a central axis to a circumferential edge of a wafer oringot; “substantially free of agglomerated intrinsic point defects”shall mean a concentration of agglomerated defects which is less thanthe detection limit of these defects, which is currently about 10³defects/cm³; “V/I boundary” means the position along the radius of aningot or wafer at which the material changes from vacancy dominated toself-interstitial dominated; and “vacancy dominated” and“self-interstitial dominated” mean material in which the intrinsic pointdefects are predominantly vacancies or self-interstitials, respectively.

EXAMPLES

[0113] As the following examples illustrate, the present inventionaffords a process for preparing a single crystal silicon ingot in which,as the ingot cools from the solidification temperature in accordancewith the Czochralski method, the agglomeration of intrinsic pointdefects is prevented within an axially symmetric region of the constantdiameter portion of the ingot, from which wafers may be sliced.

[0114] The following examples set forth one set of conditions that maybe used to achieve the desired result. Alternative approaches exist fordetermining an optimum pull rate profile for a given crystal puller. Forexample, rather than growing a series of ingots at various pull rates, asingle crystal could be grown at pull rates which increase and decreasealong the length of the crystal; in this approach, agglomeratedself-interstitial defects would be caused to appear and disappearmultiple times during growth of a single crystal. Optimal pull ratescould then be determined for a number of different crystal positions.Accordingly, the following examples should not be interpreted in alimiting sense.

Example 1 Optimization Procedure for a Crystal Puller Having aPre-Existing Hot Zone Design

[0115] A first 200 mm single crystal silicon ingot was grown underconditions in which the pull rate was ramped linearly from about 0.75mm/min. to about-0.35 mm/min. over the length of the crystal. FIG. 14shows the pull rate as a function of crystal length. Taking into accountthe pre-established axial temperature profile of a growing 200 mm ingotin the crystal puller and the pre-established radial variations in theaverage axial temperature gradient, G₀, i.e., the axial temperaturegradient at the melt/solid interface, these pull rates were selected toinsure that ingot would be vacancy dominated material from the center tothe edge at one end of the ingot and interstitial dominated materialfrom the center to the edge of the other end of the ingot. The growningot was sliced longitudinally and analyzed to determine where theformation of agglomerated interstitial defects begins.

[0116]FIG. 15 is an image produced by a scan of the minority carrierlifetime of an axial cut of the ingot over a section ranging from about635 mm to about 760 mm from the shoulder of the ingot following a seriesof oxygen precipitation heat-treatments which reveal defect distributionpatterns. At a crystal position of about 680 mm, a band of agglomeratedinterstitial defects 28 can be seen. This position corresponds to acritical pull rate of v*(680 mm)=0.33 mm/min. At this point, the widthof the axially symmetric region 6 (a region which is interstitialdominated material but which lacks agglomerated interstitial defects) isat its maximum; the width of the vacancy dominated region 8, R_(v)*(680)is about 35 mm and the width of the axially symmetric region,R_(I)*(680) is about 65 mm.

[0117] A series of four single crystal silicon ingots were then grown atsteady state pull rates which were somewhat greater than and somewhatless than the pull rate at which the maximum width of the axiallysymmetric region of the first 200 mm ingot was obtained. FIG. 16 showsthe pull rate as a function of crystal length for each of the fourcrystals, labeled, respectively, as 1-4. These four crystals were thenanalyzed to determine the axial position (and corresponding pull rate)at which agglomerated interstitial defects first appear or disappear.These four empirically determined points (marked “*”) are shown in FIG.16. Interpolation between and extrapolation from these points yielded acurve, labeled v*(Z) in FIG. 16. This curve represents, to a firstapproximation, the pull rate for 200 mm crystals as a function of lengthin the crystal puller at which the axially symmetric region is at itsmaximum width.

[0118] Growth of additional crystals at other pull rates and furtheranalysis of these crystals would further refine the empirical definitionof v*(Z).

Example 2 Reduction of Radial Variation in G₀(r)

[0119]FIGS. 17 and 18 illustrate the improvement in quality that can beachieved by reduction of the radial variation in the axial temperaturegradient at the melt/solid interface, G₀(r). The initial concentration(about 1 cm from the melt/solid interface) of vacancies andinterstitials are calculated for two cases with different G₀(r): (1)G₀(r)=2.65+5×10⁻⁴ r² (K/mm) and (2) G₀(r)=2.65+5×10⁻⁵ r² (K/mm). Foreach case the pull rate was adjusted such that the boundary betweenvacancy-rich silicon and interstitial-rich silicon is at a radius of 3cm. The pull rate used for case 1 and 2 were 0.4 and 0.35 mm/min,respectively. From FIG. 18 it is clear that the initial concentration ofinterstitials in the interstitial-rich portion of the crystal isdramatically reduced as the radial variation in the initial axialtemperature gradient is reduced. This leads to an improvement in thequality of the material since it becomes easier to avoid the formationof interstitial defect clusters due to supersaturation of interstitials.

Example 3 Increased Out-Diffusion Time for Interstitials

[0120]FIGS. 19 and 20 illustrate the improvement in quality that can beachieved by increasing the time for out-diffusion of interstitials. Theconcentration of interstitials is calculated for two cases withdiffering axial temperature profiles in the crystal, dT/dz. The axialtemperature gradient at the melt/solid interface is the same for bothcases, so that the initial concentration (about 1 cm from the melt/solidinterface) of interstitials is the same for both cases. In this example,the pull rate was adjusted such that the entire crystal isinterstitial-rich. The pull rate was the same for both cases, 0.32mm/min. The longer time for interstitial out-diffusion in case 2 resultsin an overall reduction of the interstitial concentration. This leads toan improvement in the quality of the material since it becomes easier toavoid the formation of interstitial defect clusters due tosupersaturation of interstitials.

Example 4

[0121] A 700 mm long, 150 mm diameter crystal was grown with a varyingpull rate. The pull rate varied nearly linearly from about 1.2 mm/min atthe shoulder to about 0.4 mm/min at 430 mm from the shoulder, and thennearly linearly back to about 0.65 mm/min at 700 mm from the shoulder.Under these conditions in this particular crystal puller, the entireradius is grown under interstitial-rich conditions over the length ofcrystal ranging from about 320 mm to about 525 mm from the shoulder ofthe crystal. Referring now to FIG. 21, at an axial position of about 525mm and a pull rate of about 0.47 mm/min, the crystal is free ofagglomerated intrinsic point defects clusters across the entirediameter. Stated another way, there is one small section of the crystalin which the width of the axially symmetric region, i.e., the regionwhich is substantially free of agglomerated defects, is equal to theradius of the ingot.

Example 5

[0122] As described in Example 1, a series of single crystal siliconingots were crown at varying pull rates and then analyzed to determinethe axial position (and corresponding pull rate) at which agglomeratedinterstitial defects first appeared or disappeared. Interpolationbetween and extrapolation from these points, plotted on a graph of pullrate v. axial position, yielded a curve which represents, to a firstapproximation, the pull rate for a 200 mm crystal as a function oflength in the crystal puller at which the axially symmetric region is atits maximum width. Additional crystals were then grown at other pullrates and further analysis of these crystals was used to refine thisempirically determined optimum pull rate profile.

[0123] Using this data and following this optimum pull rate profile, acrystal of about 1000 mm in length and about 200 mm in diameter wasgrown. Slices of the grown crystal, obtained from various axialposition, were then analyzed using oxygen precipitation methods standardin the art in order to (i) determine if agglomerated interstitialdefects were formed, and (ii) determine, as a function of the radius ofthe slice, the position of the V/I boundary. In this way the presence ofan axially symmetric region was determined, as well as the width of thisregion a function of crystal length or position.

[0124] The results obtained for axial positions ranging from about 200mm to about 950 mm from the shoulder of the ingot are present in thegraph of FIG. 22. These results show that a pull rate profile may bedetermined for the growth of a single crystal silicon ingot such thatthe constant diameter portion of the ingot may contain an axiallysymmetric region having a width, as measured from the circumferentialedge radially toward the central axis of the ingot, which is at leastabout 40% the length of the radius of the constant diameter portion. Inaddition, these results show that this axially symmetric region may havea length, as measured along the central axis of the ingot, which isabout 75% of the length of the constant diameter portion of the ingot.

Example 6

[0125] A single crystal silicon ingot have a length of about 1100 mm anda diameter of about 150 mm was grown with a decreasing pull rate. Thepull rate at the shoulder of the constant diameter portion of the ingotwas about 1 mm/min. The pull rate decreased exponentially to about 0.4mm/min., which corresponded to an axial position of about 200 mm fromthe shoulder. The pull rate then decreased linearly until a rate ofabout 0.3 mm/min. was reached near the end of the constant diameterportion of the ingot.

[0126] Under these process conditions in this particular hot zoneconfiguration, the resulting ingot contains a region wherein the axiallysymmetric region has a width which about equal to the radius of theingot. Referring now to FIGS. 23a and 23 b, which are images produced bya scan of the minority carrier lifetime of an axial cut of a portion ofthe following a series of oxygen precipitation heat treatments,consecutive segments of the ingot, ranging in axial position from about100 mm to about 250 mm and about 250 mm to about 400 mm are present. Itcan be seen from these figures that a region exists within the ingot,ranging in axial position from about 170 mm to about 290 mm from theshoulder, which is free of agglomerated intrinsic point defects acrossthe entire diameter. Stated another way, a region is present within theingot wherein the width of the axially symmetric region, i.e., theregion which is substantially tree of agglomerated interstitial defects,is about equal to the radius of the ingot.

[0127] In addition, in a region ranging from an axially position fromabout 125 mm to about 170 mm and from about 290 mm to greater than 400mm there are axially symmetric regions of interstitial dominatedmaterial free of agglomerated intrinsic point defects surrounding agenerally cylindrical core of vacancy dominated material which is alsofree of agglomerated intrinsic point defects.

[0128] Finally, in a region ranging from an axially position from about100 mm to about 125 mm there is an axially symmetric region ofinterstitial dominated material free of agglomerated defects surroundinga generally cylindrical core of vacancy dominated material. Within thevacancy dominated material, there is an axially symmetric region whichis free of agglomerated defects surrounding a core containingagglomerated vacancy defects.

Example 7 Cooling Rate and Position of V/I Boundary

[0129] A series of single crystal silicon ingots (150 mm and 200 mmnominal diameter), were grown in accordance with the Czochralski methodusing different hot zone configurations, designed by means common in theart, which affected the residence time of the silicon at temperatures inexcess of about 1050° C. The pull rate profile for each ingot was variedalong the length of the ingot in an attempt to create a transition froma region of agglomerated vacancy point defects to a region ofagglomerated interstitial point defects.

[0130] Once grown, the ingots were cut longitudinally along the centralaxis running parallel to the direction of growth, and then furtherdivided into sections which were each about 2 mm in thickness. Using thecopper decoration technique previously described, one set of suchlongitudinal sections was then heated and intentionally contaminatedwith copper, the heating conditions being appropriate for thedissolution of a high concentration of copper interstitials. Followingthis heat treatment, the samples were then rapidly cooled, during whichtime the copper impurities either outdiffused or precipitated at siteswhere oxide clusters or agglomerated interstitial defects where present.After a standard defect delineating etch, the samples were visuallyinspected for the presence of precipitated impurities; those regionswhich were free of such precipitated impurities corresponded to regionswhich were free of agglomerated interstitial defects.

[0131] Another set of the longitudinal sections was subjected to aseries of oxygen precipitation heat treatments in order to cause thenucleation and growth of new oxide clusters prior to carrier lifetimemapping. Contrast bands in lifetime mapping were utilized in order todetermine and measure the shape of the instantaneous melt/solidinterface at various axial positions in each ingot. Information on theshape of the melt/solid interface was then used, as discussed furtherbelow, to estimate the absolute value of, and the radial variation in,the average axial temperature gradient, G₀. This information was alsoused, in conjunction with the pull rate, to estimate the radialvariation in v/G₀.

[0132] To more closely examine the effect growth conditions have on theresulting quality of a single crystal silicon ingot, several assumptionswere made which, based on experimental evidence available to-date, arebelieved to be justified. First, in order to simplify the treatment ofthermal history in terms of the time taken to cool to a temperature atwhich the agglomeration of interstitial defects occurs, it was assumedthat about 1050° C. is a reasonable approximation for the temperature atwhich the agglomeration of silicon self-interstitials occurs. Thistemperature appears to coincide with changes in agglomeratedinterstitial defect density observed during experiments in whichdifferent cooling rates were employed. Although, as noted above, whetheragglomeration occurs is also a factor of the concentration ofinterstitials, it is believed that agglomeration will not occur attemperatures above about 1050° C. because, given the range ofinterstitial concentrations typical for Czochralski-type growthprocesses, it is reasonable to assume that the system will not becomecritically supersaturated with interstitials above this temperature.Stated another way, for concentrations of interstitials which aretypical for Czochralski-type growth processes, it is reasonable toassume that the system will not become critically supersaturated, andtherefore an agglomeration event will not occur, above a temperature ofabout 1050° C.

[0133] The second assumption that was made to parameterize the effect ofgrowth conditions on the quality of single crystal silicon is that thetemperature dependence of silicon self-interstitial diffusivity isnegligible. Stated another way, it is assumed that self-interstitialsdiffuse at the same rate at all temperatures between about 1400° C. andabout 1050° C. Understanding that about 1050° C. is considered areasonable approximation for the temperature of agglomeration, theessential point of this assumption is that the details of the coolingcurve from the melting point does not matter. The diffusion distancedepends only on the total time spent cooling from the melting point toabout 1050° C.

[0134] Using the axial temperature profile data for each hot zone designand the actual pull rate profile for a particular ingot, the totalcooling time from about 1400° C. to about 1050° C. may be calculated. Itshould be noted that the rate at which the temperature changes for eachof the hot zones was reasonably uniform. This uniformity means that anyerror in the selection of a temperature of nucleation for agglomeratedinterstitial defects, i.e. about 1050° C., will arguably lead only toscaled errors in the calculated cooling time.

[0135] In order to determine the radial extent of the vacancy dominatedregion of the ingot (R_(vacancy)), or alternatively the width of theaxially symmetric region, it was further assumed that the radius of thevacancy dominated core, as determined by the lifetime map, is equivalentto the point at solidification where v/G₀=v/G₀ critical. Stated anotherway, the width of the axially symmetric region was generally assumed tobe based on the position of the V/I boundary after cooling to roomtemperature. This is pointed out because, as mentioned above, as tileingot cools recombination of vacancies and silicon self-interstitialsmay occur. When recombination does occur, the actual position of the V/Iboundary shifts inwardly toward the central axis of the ingot. It isthis final position which is being referred to here.

[0136] To simplify the calculation of G₀, the average axial temperaturegradient in the crystal at the time of solidification, the melt/solidinterface shape was assumed to be the melting point isotherm. Thecrystal surface temperatures were calculated using finite elementmodeling (FEA) techniques and the details of the hot zone design. Theentire temperature field within the crystal, and therefore G₀, wasdeduced by solving Laplace's equation with the proper boundaryconditions, namely, the melting point along the melt/solid interface andthe FEA results for the surface temperature along the axis of thecrystal. The results obtained at various axial positions from one of theingots prepared and evaluated are presented in FIG. 25.

[0137] To estimate the effect that radial variations in G₀. have on theinitial interstitial concentration, a radial position R′, that is, aposition halfway between the V/I boundary and the crystal surface, wasassumed to be the furthest point a silicon self-interstitial can be froma sink in the ingots whether that sink be in the vacancy dominatedregion or on the crystal surface. By using the growth rate and the G₀data for the above ingot, the difference between the calculated v/G₀ atthe position R′ and v/G₀ at the V/I boundary (i.e., the critical v/G₀value) provides an indication of the radial variation in the initialinterstitial concentration, as well as the effect this has on theability for excess interstitials to reach a sink on the crystal surfaceor in the vacancy dominated region.

[0138] For this particular data set, it appears there is no systematicdependence of the quality of the crystal on the radial variation inv/G₀. As can be seen in FIG. 26, the axial dependence in the ingot isminimal in this sample. The growth conditions involved in this series ofexperiments represent a fairly narrow range in the radial variation ofG₀. As a result, this data set is too narrow to resolve a discernabledependence of the quality (i.e., the presence of absence of a band ofagglomerated intrinsic point defects) on the radial variation of G₀.

[0139] As noted, samples of each ingot prepared were evaluated atvarious axial positions for the present or absence of agglomeratedinterstitial defects. For each axial position examined, a correlationmay be made between the quality of the sample and the width of theaxially symmetric region. Referring now to FIG. 27, a graph may beprepared which compares the quality of the given sample to the time thesample, at that particular axial position, was allowed to cool fromsolidification to about 1050° C. As expected, this graph shows the widthof the axially symmetric region (i.e., R_(crystal)−R_(vacancy)) has astrong dependence on the cooling history of the sample within thisparticular temperature range. In order of the width of the axiallysymmetric region to increase, the trend suggests that longer diffusiontimes, or slower cooling rates, are needed.

[0140] Based on the data present in this graph, a best fit line may becalculated which generally represents a transition in the quality of thesilicon from “good” (i.e., defect-free) to “bad” (i.e., containingdefects), as a function of the cooling time allowed for a given ingotdiameter within this particular temperature range. This generalrelationship between the width of the axially symmetric region and thecooling rate may be expressed in terms of the following equation:

(R _(crystal) −R _(transistion))² =D _(eff) t _(1050° C.)

[0141] wherein

[0142] R_(crystal) is the radius of the ingot,

[0143] R_(transition) is the radius of the axially symmetric region atan axial position in the sample were a transition occurs in theinterstitial dominated material from being defect-free to containingdefects, or vice versa,

[0144] D_(eff) is a constant, about 9.3*10⁻⁴ cm²sec⁻¹, which representsthe average time and temperature of interstitial diffusivity, and

[0145] t_(1050° C.) is the time required for the given axial position ofthe sample to cool from solidification to about 1050° C.

[0146] Referring again to FIG. 27, it can be seen that, for a giveningot diameter, a cooling time may be estimated in order to obtain anaxially symmetric region of a desired diameter. For example, for aningot having a diameter of about 150 mm, an axially symmetric regionhaving a width about equal to the radius of the ingot may be obtainedif, between the temperature range of about 1410° C. and about 1050° C.,this particular portion of the ingot is allowed to cool for about 10 toabout 15 hours. Similarly, for an ingot having a diameter of about 200mm, an axially symmetric region having a width about equal to the radiusof the ingot may be obtained if between this temperature range thisparticular portion of the ingot is allowed to cool for about 25 to about35 hours. If this line is further extrapolated, cooling times of about65 to about 75 hours may be needed in order to obtain an axiallysymmetric region having a width about equal to the radius of an ingothaving a diameter of about 300 mm. It is to be noted in this regardthat, as the diameter of the ingot increases, additional cooling time isrequired due to the increase in distance that interstitials must diffusein order to reach sinks at the ingot surface or the vacancy core.

[0147] Referring now to FIGS. 28, 29, 30 and 31, the effects ofincreased cooling time for various ingots may be observed. Each of thesefigures depicts a portion of a ingot having a nominal diameter of 200mm, with the cooling time from the temperature of solidification to1050° C. progressively increasing from FIG. 28 to FIG. 31.

[0148] Referring to FIG. 28, a portion of an ingot, ranging in axialposition from about 235 mm to about 350 mm from the shoulder, is shown.At an axial position of about 255 mm, the width of the axially symmetricregion free of agglomerated interstitial defects is at a maximum, whichis about 45% of the radius of the ingot. Beyond this position, atransition occurs from a region which is free of such defects, to aregion in which such defects are present.

[0149] Referring now to FIG. 29, a portion of an ingot, ranging in axialposition from about 305 mm to about 460 mm from the shoulder, is shown.At an axial position of about 360 mm, the width of the axially symmetricregion free of agglomerated interstitial defects is at a maximum, whichis about 65% of the radius of the ingot. Beyond this position, defectformation begins.

[0150] Referring now to FIG. 30, a portion of an ingot, ranging in axialposition from about 140 mm to about 275 mm from the shoulder, is shown.At an axial position of about 210 mm, the width of the axially symmetricregion is about equal to the radius of the ingot; that is, a smallportion of the ingot within this range is free of agglomerated intrinsicpoint defects.

[0151] Referring now to FIG. 31, a portion of an ingot, ranging in axialposition from about 600 mm to about 730 mm from the shoulder, is shown.Over an axial position ranging from about 640 mm to about 605 mm, thewidth of the axially symmetric region is about equal to the radius ofthe ingot. In addition, the length of the ingot segment in which thewidth of the axially symmetric region is about equal to the radius ofthe ingot is greater than what is observed in connection with the ingotof FIG. 30.

[0152] When viewed in combination, therefore, FIGS. 28, 29, 30, and 31demonstrate the effect of cooling time to 1050° C. upon the width andthe length of the defect-free, axially symmetric region. In general, theregions containing agglomerated interstitial defects occurred as aresult of a continued decrease of the crystal pull rate leading to aninitial interstitial concentration which was too large to reduce for thecooling time of that portion of the crystal. A greater length of theaxially symmetric region means a larger range of pull rates (i.e.,initial interstitial concentration) are available for the growth of suchdefect-free material. Increasing the cooling time allows for initiallyhigher concentration of interstitials, as sufficient time for radialdiffusion may be achieved to suppress the concentration below thecritical concentration required for agglomeration of interstitialdefects. Stated in other words, for longer cooling times, somewhat lowerpull rates (and, therefore, higher initial interstitial concentrations)will still lead to maximum axially symmetric region 6. Therefore, longercooling times lead to an increase in the allowable pull rate variationabout the condition required for maximum axially symmetric regiondiameter and ease the restrictions on process control. As a result, theprocess for an axially symmetric region over large lengths of the ingotbecomes easier.

[0153] Referring again to FIG. 31, over an axial position ranging fromabout 665 mm to greater than 730 mm from the shoulder of crystal, aregion of vacancy dominated material free of agglomerated defects ispresent in which the width of the region is equal to the radius of theingot.

[0154] As can be seen from the above data, by means of controlling thecooling rate, the concentration of self-interstitials may be suppressedby allowing more time for interstitials to diffuse to regions where theymay be annihilated. As a result, the formation of agglomeratedinterstitial defects is prevented within significant portion of thesingle crystal silicon ingot.

[0155] In view of the above, it will be seen that the several objects ofthe invention are achieved.

[0156] As various changes could be made in the above compositions andprocesses without departing from the scope of the invention, it isintended that all matter contained in the above description beinterpreted as illustrative and not in a limiting sense.

What is claimed is:
 1. A process for growing a single crystal siliconingot in which the ingot comprises a central axis, a seed-cone, anend-cone and a constant diameter portion between the seed-cone and theend-cone having a circumferential edge and a radius extending from thecentral axis to the circumferential edge, the ingot being grown from asilicon melt and then cooled from the solidification temperature inaccordance with the Czochralski method, the process comprisingcontrolling (i) a growth velocity, v, (ii) an average axial temperaturegradient, G₀, during the growth of the constant diameter portion of thecrystal over the temperature range from solidification to a temperatureof no less than about 1325° C., and (iii) the cooling rate of thecrystal from the solidification temperature to about 1,050° C. to causethe formation of an axially symmetrical segment which is substantiallyfree of agglomerated intrinsic point defects wherein the axiallysymmetric region extends inwardly from the circumferential edge of theingot, has a width as measured from the circumferential edge radiallytoward the central axis of the ingot which is at least aboutthree-tenths the length of the radius of the ingot, and has a length asmeasured along the central axis of at least about two-tenths the lengthof the constant diameter portion of the ingot.
 2. The process of claim 1wherein the crystal has a nominal diameter of about 150 mm and is cooledfrom the solidification temperature to a temperature of at least about1,050° C. over a period of at least about 10 hours.
 3. The process ofclaim 1 wherein the crystal has a nominal diameter of about 150 mm andis cooled from the solidification temperature to a temperature of atleast about 1,050° C. over a period of at least about 15 hours.
 4. Theprocess of claim 1 wherein the crystal has a nominal diameter of about200 mm and is cooled from the solidification temperature to atemperature of at least about 1,050° C. over a period of at least about10 hours.
 5. The process of claim 1 wherein the crystal has a nominaldiameter of about 200 mm and is cooled from the solidificationtemperature to a temperature of at least about 1,050° C. over a periodof at least about 20 hours.
 6. The process of claim 1 wherein thecrystal has a nominal diameter of greater than 200 mm and is cooled fromthe solidification temperature to a temperature of at least about 1,050°C. over a period of at least about 40 hours.
 7. The process of claim 1wherein the crystal has a nominal diameter of greater than 200 mm and iscooled from the solidification temperature to a temperature of at leastabout 1,050° C. over a period of at least about 60 hours.
 8. The processof claim 1 wherein the length of the axially symmetric region is atleast about three-tenths the length of the constant diameter portion ofthe ingot.
 9. The process of claim 8 wherein the crystal has a nominaldiameter of about 150 mm and is cooled from the solidificationtemperature to a temperature of at least about 1,050° C. over a periodof at least about 10 hours.
 10. The process at claim 8 wherein thecrystal has a nominal diameter of about 150 mm and is cooled from thesolidification temperature to a temperature of at least about 1,050° C.over a period of at least about 15 hours.
 11. The process of claim 8wherein the crystal has a nominal diameter of about 200 mm and is cooledfrom the solidification temperature to a temperature of at least about1,050° C. over a period of at least about 10 hours.
 12. The process ofclaim 8 wherein the crystal has a nominal diameter of about 200 mm, andis cooled from the solidification temperature to a temperature of atleast about 1,050° C. over a period of at least about 20 hours.
 13. Theprocess of claim 8 wherein the crystal has a nominal diameter of greaterthan 200 mm and is cooled from the solidification temperature to atemperature of at least about 1,050° C. over a period of at least about40 hours.
 14. The process of claim 8 wherein the crystal has a nominaldiameter of greater than 200 mm and is cooled from the solidificationtemperature to a temperature of at least about 1,050° C. over a periodof at least about 60 hours.
 15. The process of claim 1 wherein thegrowth velocity, v, and the instantaneous axial temperature gradient,G₀, are controlled such that the ratio, v/G₀, ranges in value from about0.6 to about 1.5 times the critical value of v/G₀.
 16. The process ofclaim 1 wherein the growth velocity, v, and the instantaneous axialtemperature gradient, G₀, are controlled such that the ratio v/G₀ rangesin value from about 0.75 to about 1 times the critical value of v/G₀.17. The process of claim 1 wherein the average axial temperaturegradient, G₀, is controlled over the temperature range fromsolidification to a temperature of no less than about 1350° C.
 18. Theprocess of claim 17 the crystal has a nominal diameter of about 150 mmand is cooled from the solidification temperature to a temperature of atleast about 1,050° C. over a period of at least about 15 hours.
 19. Theprocess of claim 17 the crystal has a nominal diameter of about 200 mmand is cooled from the solidification temperature to a temperature of atleast about 1,050° C. over a period of at least about 15 hours.
 20. Theprocess of claim 17 the crystal has a nominal diameter of greater than200 mm and is cooled from the solidification temperature to atemperature of at least about 1,050° C. over a period of at least about40 hours.